• Structural Engineering and Mechanics
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• v.8 no.2
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• pp.151-164
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• 1999

The large deflection theory of the Mindlin plate and Galerkin's method are employed to examine the static responses of a plate produced by the weight of the plate, and the dynamic responses of the plate caused by the coupling effect of these static responses with a set of moving forces. Results obtained by the large deflection theory are compared with those by the small deflection theory. The results indicate that the effect of weight of the plate increases the modal frequencies of the structure. The deviations of dynamic transverse deflection and of dynamic bending moment produced by a moving concentrated force between the two theories are significant for a thin plate with a large area. Both dynamic transverse deflection and dynamic bending moment obtained by the Mindlin plate theory are greater than those by the classical plate.

• Transactions of Materials Processing
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• v.3 no.4
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• pp.401-414
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• 1994

Springback for the three point bending is anlayzed and experimented. Neutral axis is assumed to remain at the midthickness for large ratio of radius of curvature to thickness. Pure bending theory is used to be extended to the analysis of the springback for three point bending. The specimen is thought to be divided into numerous small elements. The theory for pure bending is then adopted for analysis of each element to obtain springback in terms of the relationship between initial and final deflections. the boundary conditions between neighborhood elements are the deflection and slope which should be the same. Deflection is calculated by summing up the deflections of each element. Experiments have been performed for different conditions which are punch radius, span length, and initial deflections. Comparisons between the analytical solution and experimental results show the same trends.

• Steel and Composite Structures
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• v.14 no.6
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• pp.605-620
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• 2013

This paper provides an innovative iteration technique for the large deflection problem of annular plate. After some manipulation, the problem is reduced to a couple of ODEs (ordinary differential equation). Among them, one is derived from the plane stress problem for plate, and other is derived from the bending of plate. Since the large deflection for plate is assumed in the problem, the relevant non-linear terms appear in the resulting ODEs. The pseudo-linearization procedure is suggested to solve the problem and the nonlinear ODEs can be solved in the way for the solution of linear ODE. To obtain the final solution, it is necessary to use the iteration. Several numerical examples are provided. In the study, the assumed value for non-dimensional loading is larger than those in the available references.

• Structural Engineering and Mechanics
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• v.51 no.2
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• pp.333-347
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• 2014

Nonlinear bending of super-elliptical plates of uniform thickness under uniform transverse pressure was investigated by the Ritz method. The material was assumed to be homogeneous and isotropic. The contribution of the boundary conditions at the point supports was introduced by the Lagrange multipliers. The solution was obtained by the Newton-Raphson method. The influence of the location of the point supports on the central deflection was highlighted by sensitivity analysis. An approximate relationship between the central deflection and the super-elliptical power was obtained using the method of least squares. The critical points where the maximum deflection may develop, and the influence of nonlinearity were highlighted. The nonlinearity was found to be sensitive to the aspect ratio. The accuracy of the algorithm was validated by comparing the central deflection with the solutions of elliptical and rectangular plates.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1889-1900
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• 1995

In this study, a large deflection analysis of a plane frame composed of a thin-walled tube in investigated. When bent, a thin-walled tube is usually controlled by local buckling and subsequent bending collapse of the section. So load resistance reaches the yield level in a thin-walled rectangular tube. This relationship can be divided into three regimes : elastic, post-buckling and crippling. In this paper, this relationship is theoretically presented to be capable of describing nonlinearities and a stiffness matrix is derived by introducing a compound beam-spring element. A numerical analysis uses a constant incremental energy method and the solution is obtained by modifying stiffness matrix at elastic/inelastic stage. This analytical results, load-deflection paths show a good agreement with the test results.

• Steel and Composite Structures
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• v.42 no.1
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• pp.23-32
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• 2022

In this paper, a nonlinear numerical method to solve the large deflection problem is introduced. And the non-dimensional load-deflection behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is parametrically investigated. The large deflection problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)^* hierarchical model, and it is approximated by 2-D natural element method (NEM). The shear locking phenomenon is suppressed by the selectively reduced integration method. The nonlinear matrix equations are solved by combining the incremental loading scheme and the Newton-Raphson iteration method. The proposed method is validated from the benchmark experiments, where the propose method shows an excellent agreement with the reference methods. The nonlinear behavior of FG-CNTRC plates is evaluated in terms of the non-dimensional load-deflection curve, and it is parametrically investigated with respect to the existence/non-existence and gradient pattern of CNTs, the width-to-thickness and aspect ratios of plates and the type of boundary conditions. The non-dimensional central deflection is significantly reduced when CNTs and added, and it decreases with the volume fraction of CNTs. But, it shows a uniform increase in proportion to the width-to-thickness and aspect ratios. Both the gradient pattern of CNTs and the type of boundary conditions do also show the remarkable effects.

• Journal of the Semiconductor & Display Technology
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• v.7 no.4
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• pp.1-5
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• 2008

There is a need to enlarge the mother glass substrate in OLED to raise its productivity and to realize OLED TV. On the other hand, some difficulties may arise regarding the deflection of a large glass substrate during its handling operation due to its thinness $(0.5\sim0.7t)$, which is not even enough to allow it to stand its own mass. This thesis proposes a conceptual plan for the application of the clamping- and bending-end conditions to the glass substrate handler. To verify proposed plan, the non-contact 3 dimensional measuring instrument is developed. The composition of the 3 dimensional measuring instrument measures shape of the product using X-Y stage robot and laser distance sensor. X-Y stage robot and laser distance sensor are controlled by LabVIEW language. To calibrate measuring instrument, the direction conversion of the Euler angle was used. In order to confirm deflection of the glass substrate, the experiment was carried out at the bending end boundary condition and the proposed effect was verified.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1896-1901
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• 2008

Single crystalline copper nanowires are subjected to bending tests using molecular dynamics simulations and the embedded atom method. To observe behaviors of nanowire, bending tests are performed for various rates of deflection and different boundary conditions: fixed-free and fixed-fixed. When the deflection of nanowire becomes large, twinnings and dislocations appear, and <100> crystal structure transforms to <110>. At high rates, phase transformation occurs in whole nanowire. But, at low rates, atomic structure changes to <110> phase partially. The final deformed structures are affected by the rate of deflection and boundary conditions. These effects can be important design parameters at nanoscale.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.3
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• pp.68-74
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• 2001

In the drawing of large size automotive panels, elastic deflection of die components is induced by the contact force between them. The deflection is nonuniform and locally distributed, and results in nonuniform material flow. In order to arrange such a nonuniform die gap, a correcting operation, so called die spotting, is inevitable, which requires trial and error works and consuming time. A prediction of the bending deflection prior to a try-out must be useful to reduce the die spotting time. In this study, drawing process of a front fender is simulated first. and the deflection of the blank holder is calculated from the contact force imposing on th blank holder. The balance block heights ensuring a uniform deflection are optimized by the analysis and design of experiments.

• Structural Engineering and Mechanics
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• v.44 no.3
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• pp.405-416
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• 2012

In this study the investigation of large deflections subject in compliant mechanisms is presented using homotopy perturbation method (HPM). The main purpose is to propose a convenient method of solution for the large deflection problem in compliant mechanisms in order to overcome the difficulty and complexity of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, a cantilever beam of linear elastic material under horizontal, vertical and bending moment end point load is considered. The results show that the applied method is very accurate and capable for cantilever beams and can be used for a large category of practical problems for the aim of optimization. Also the consequence of effective parameters on the large deflection is analyzed and presented.